Volume 17, Issue 5
Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition

Qingjie Hu, Yinnian He & Kun Wang

Int. J. Numer. Anal. Mod., 17 (2020), pp. 643-661.

Published online: 2020-08

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  • Abstract

In this article, we consider a weak Galerkin finite element method for the two dimensional exterior Helmholtz problem. After introducing a nonlocal boundary condition by means of the exact Dirichlet to Neumann (DtN) operator for the exterior problem, we prove that the existence and uniqueness of the weak Galerkin finite element solution for this problem. Then, applying some projection techniques, we establish a priori error estimate, which include the effect of truncation of the DtN boundary condition as well as the spatial discretization. Finally, some numerical examples are presented to confirm the theoretical predictions.

  • Keywords

Helmholtz equation, weak Galerkin method, Dirichlet to Neumann operator, error estimates.

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COPYRIGHT: © Global Science Press

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@Article{IJNAM-17-643, author = {Hu , Qingjie and He , Yinnian and Wang , Kun}, title = {Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2020}, volume = {17}, number = {5}, pages = {643--661}, abstract = {

In this article, we consider a weak Galerkin finite element method for the two dimensional exterior Helmholtz problem. After introducing a nonlocal boundary condition by means of the exact Dirichlet to Neumann (DtN) operator for the exterior problem, we prove that the existence and uniqueness of the weak Galerkin finite element solution for this problem. Then, applying some projection techniques, we establish a priori error estimate, which include the effect of truncation of the DtN boundary condition as well as the spatial discretization. Finally, some numerical examples are presented to confirm the theoretical predictions.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/17873.html} }
TY - JOUR T1 - Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition AU - Hu , Qingjie AU - He , Yinnian AU - Wang , Kun JO - International Journal of Numerical Analysis and Modeling VL - 5 SP - 643 EP - 661 PY - 2020 DA - 2020/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/17873.html KW - Helmholtz equation, weak Galerkin method, Dirichlet to Neumann operator, error estimates. AB -

In this article, we consider a weak Galerkin finite element method for the two dimensional exterior Helmholtz problem. After introducing a nonlocal boundary condition by means of the exact Dirichlet to Neumann (DtN) operator for the exterior problem, we prove that the existence and uniqueness of the weak Galerkin finite element solution for this problem. Then, applying some projection techniques, we establish a priori error estimate, which include the effect of truncation of the DtN boundary condition as well as the spatial discretization. Finally, some numerical examples are presented to confirm the theoretical predictions.

Qingjie Hu, Yinnian He & Kun Wang. (2020). Weak Galerkin Method for the Helmholtz Equation with DtN Boundary Condition. International Journal of Numerical Analysis and Modeling. 17 (5). 643-661. doi:
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